Question

What is the equation of a line passing through (-3,7) with a slope of -1/5?

Answer 1

Put it into point-slope form:

y-y1= m(x-x1)

(x1,y1) <== the points m<== the slope Keep the other x and y the same.

y-7= -1/5(x-(-3)
y-7=-1/5(x+3)

We can multiply everything by -5, to get a constant number.

y-35=1(-5x-15)
-5y-35= -5x-15

Add 35 to both sides.

-5y=-5x+20

We can put this in standard form as well.

Ax+By= C

Subtract 20 on both sides.

-5y-20= -5x

Add 5y to the other sides.

-20=-5x+5y or -5x+5y=-20 <== standard form

I hope this helps!
~kaikers

Answer 2

You are trying to find a line that has a general equation of
y = mx + b
You know what m is because it is given as the slope.
m = - 1/5

y = - 1/5 x + b
Now to use the point to find b
y = 7
x = - 3

7 = -1/5 (-3) + b
7 = 3/5 + b look out for those nasty minus signs. There are 2 of them and they turn into plus.
7 - 3/5 = b
b = 6 2/5 = 6.4

Change m to -0.2
So y = -0.2 x + 6.4